A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation

DOI10.1515/demo-2019-0003zbMath1434.62045arXiv1810.06227OpenAlexW2897342257WikidataQ128298104 ScholiaQ128298104MaRDI QIDQ2283661

Julyan Arbel, Caroline Lawless

Publication date: 13 January 2020

Published in: Dependence Modeling (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.06227

zbMATH Keywords

partitionsclusteringBayesian nonparametricsPitman-Yor processstick-breaking process

Mathematics Subject Classification ID

Density estimation (62G07) Foundations of stochastic processes (60G05) Probability theory (educational aspects) (97K50)

Uses Software

• plfit

Cites Work

• Unnamed Item
• Unnamed Item
• Model-based clustering using copulas with applications
• Beta-product dependent Pitman-Yor processes for Bayesian inference
• Bayesian semiparametric inference for multivariate doubly-interval-censored data
• Some diffusion processes associated with two parameter Poisson-Dirichlet distribution and Dirichlet process
• On a class of Bayesian nonparametric estimates: I. Density estimates
• Two-parameter family of infinite-dimensional diffusions on the Kingman simplex
• Adaptive Bayesian density estimation in \(L^p\)-metrics with Pitman-Yor or normalized inverse-Gaussian process kernel mixtures
• Size-biased sampling of Poisson point processes and excursions
• Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems
• The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
• A characterization of product-form exchangeable feature probability functions
• An elementary derivation of the Chinese restaurant process from Sethuraman's stick-breaking process
• On the Markov-Krein identity and quasi-invariance of the gamma process
• Exchangeable and partially exchangeable random partitions
• Stochastic approximations to the Pitman-Yor process
• A Bayesian analysis of some nonparametric problems
• Inconsistency of Pitman-Yor process mixtures for the number of components
• Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics
• Heterogeneous reciprocal graphical models
• Random-energy model: An exactly solvable model of disordered systems
• Power-Law Distributions in Empirical Data
• Bayesian Non-Parametric Inference for Species Variety with a Two-Parameter Poisson–Dirichlet Process Prior
• Gibbs Sampling Methods for Stick-Breaking Priors
• Some issues in nonparametric Bayesian modeling using species sampling models
• On the Pitman–Yor process with spike and slab base measure
• Fundamentals of Nonparametric Bayesian Inference

This page was built for publication: A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation